Start off maths exam in lesson (5)
I believe the answer is:
moral
'lesson' is the definition.
(as in the moral of the story)
'start off maths exam' is the wordplay.
'start off' suggests taking the first letters.
'exam' becomes 'oral' (spoken academic test).
The initial letter of 'maths' is 'm'.
'm'+'oral'='MORAL'
'in' is the link.
(Other definitions for moral that I've seen before include "Virtuous and principled" , "Behaving ethically" , "ethical principle" , "Practical lesson to be drawn from an experience" , "Honourable" .)